Questions tagged [semi-simple-rings]

Let $M\neq \{0\}$ be a semi-simple left $R$ module .Prove that it contains a simple sub-module. An $R-$ module $M$ is said to be semi-simple if every submodule of $M$ is a direct summand of M My solution Since $M\neq \{0\}$; $\exists m\in M$ such…

I'm working on an expository paper and need a little clarification. Let $R = \mathbb{M}_n(D)$ where $D$ is a division ring. Let $E_{ij}$ be the matix whose $(i,j)$-entry is 1 and all other are zeros. Then, $R = {\bf a_1} \oplus \cdots \oplus {\bf…

I am studying Semi-Simple Rings from "A first course in Non-Commutative Rings " by T.Y.Lam . But hardly I am finding any examples to the definitions that are being taught.There is no example of a semisimple ring only the definition is provided i.e…